SECTION 44 BASIC STATISTICAL METHODS
Edward J. Dudewicz
Department of Mathematics,
Syracuse University, Syracuse, New York
THE STATISTICAL TOOL KIT 44.2
SOURCES AND SUMMARIZATION OF DATA
44.2
Planning for Collection and Analysis of
Data 44.2
Historical Data, Their Uses, and Caveats
44.4
Data from Planned Experimentation 44.5
Data Screening 44.5
Descriptive Statistics for Summarizing
Data 44.7
Accurate Calculation of Descriptive
Statistics 44.15
PROBABILITY MODELS FOR EXPERIMENTS
44.17
Sample Space 44.18
Events 44.18
Rules of Probability, Combinatorics 44.20
Conditional Probability; Bayes’ Theorem
44.21
DISCRETE PROBABILITY DISTRIBUTIONS
44.23
The Discrete Uniform Distribution 44.23
The Binomial Distribution 44.24
The Hypergeometric Distribution 44.24
The Poisson Distribution 44.25
The Negative Binomial Distribution 44.26
The Multinomial Distribution 44.27
Selecting a Discrete Distribution 44.27
CONTINUOUS PROBABILITY
DISTRIBUTIONS 44.28
The Continuous Uniform Distribution
44.28
The Exponential Distribution 44.29
The Weibull Distribution 44.31
The Normal Distribution 44.33
The Lognormal Distribution 44.36
Mixture Distributions 44.37
The Multinormal Distribution 44.39
The Extended Generalized Lambda
Distribution 44.39
Selecting a Continuous Distribution
44.40
Bootstrap Methods 44.41
STATISTICAL ESTIMATION 44.41
Point Estimates 44.42
Confidence Interval Estimates 44.42
Prediction Intervals 44.47
Tolerance Intervals 44.47
Bayesian Estimates 44.54
Intervals with Fixed Width and Precision
44.54
STATISTICAL TESTS OF HYPOTHESES
44.58
Basic Concepts, Types of Errors 44.58
Use of the Operating Characteristic Curve
in Selecting an Acceptance Region
44.59
Testing a Hypothesis When the Sample
Size Is Fixed in Advance 44.61
Testing a Hypothesis When the Sample
Size Is Not Fixed in Advance 44.74
Drawing Conclusions from Tests of
Hypotheses 44.77
Determining the Sample Size Required
for Testing a Hypothesis 44.78
Relation to Confidence Intervals 44.79
Standard Cases 44.80
Statistical Significance versus Practical
Significance 44.80
ADDITIONAL STATISTICAL TOOLS 44.81
Transformations of Data 44.81
Monte Carlo Sampling Methods 44.84
Bootstrap Methods 44.84
The Generalized Bootstrap 44.85
Clustering and Discrimination 44.86
Heteroscedastic Discrimination 44.86
Selection of the Best versus Testing
Hypotheses 44.87
REGRESSION AND CORRELATION
ANALYSIS 44.88
Simple Linear Regression 44.91
Residuals, Outliers, Confidence and
Prediction Bands, Extrapolation; Lack of
Fit—Replicated Observations 44.96
Confidence Intervals 44.97
Multiple Regression 44.98
REFERENCES 44.108
SECTION 45 STATISTICAL PROCESS CONTROL
Harrison M. Wadsworth
INTRODUCTION 45.1
Definitions 45.2
Notation 45.2
THEORY AND BACKGROUND OF
STATISTICAL PROCESS CONTROL 45.2
STEPS TO START A CONTROL CHART 45.4
CONSTRUCTING A CONTROL CHART FOR
VARIABLES FOR ATTAINING A STATE OF
CONTROL (NO STANDARD GIVEN
CHARTS) 45.5
X and R Charts 45.5
s Charts 45.7
INTERPRETATION OF CONTROL CHARTS
45.7
CONTROL CHARTS FOR INDIVIDUALS 45.10
Computing the Control Limits 45.11
Moving Range 45.11
Standard Deviation 45.11
CONSTRUCTING CONTROL CHARTS FOR
VARIABLES WHEN A STANDARD IS
GIVEN 45.12
CONTROL CHARTS FOR ATTRIBUTES
45.12
Control Charts for Percentage
Nonconforming (p) 45.12
Control Charts for Number of
Nonconforming Items (np) 45.14
Control Charts for Number of
Nonconformities (c) 45.15
Control Chart for Number of
Nonconformities per Item (u) 45.15
CUMULATIVE SUM (CUSUM) CONTROL
CHARTS 45.17
Construction of a CUSUM Control Chart
for Averages 45.17
CUSUM Limits Using the Tabulation
Method 45.20
THE EXPONENTIALLY WEIGHTED MOVING
AVERAGE CONTROL CHART 45.20
SHORT-RUN CONTROL CHARTS 45.23
BOX-JENKINS MANUAL ADJUSTMENT
CHART 45.24
MULTIVARIATE CONTROL CHARTS 45.25
PRE-CONTROL 45.25
STATISTICAL CONTROL OF AUTOMATED
PROCESSES 45.27
Software for Statistical Process Control
45.27
REFERENCES 45.28
SECTION 47 DESIGN AND ANALYSIS OF EXPERIMENTS
J. Stuart Hunter
with Mary G. Natrella, E. Harvey Barnett,
William G. Hunter, and Truman L. Koehler
SECTION 48 RELIABILITY CONCEPTS AND DATA ANALYSIS
William Q. Meeker
Luis A. Escobar
Necip Doganaksoy
Gerald J. Hahn
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